Question

Consider the spot in which you can strike a pool ball with a cue so that there is no friction between the ball and the surface.

14 h G FIG. 1: A physics student strikes a pool ball with a cue Note: the line from G points to the location of the center of mass, and P represents the point of contact between the ball and the table. Use only concepts from Ch 12 and before to solve the following: 1. (25 points) Given the parameters in the figure above, find h Hint: consider Newton's laws acting on the ball while it is being struck by the cue. You can assume the force of the cue on the ball is constant in time. 2. (20 points) Now assume you strike the ball (mass, m) a distance 4r below h with an average force, Fav, for a time interval, At. Find the velocity ; and the angular velocity Wiimmediately after the strike. 3. (10 points) Given the coefficient of kinetic friction k between the ball and the table, what is the acceleration of the center of mass, āc, and the rotational acceleration, a, of ball while it is slipping? 4. (5 points) Find the velocity of the center of mass, üc(t) and the angular velocity of the ball about its center of mass, w(t), as functions of time as it slides 5. (10 points) How far (distance) does the ball slide before it stops sliding (and starts rolling) in terms of any necessary previously given parameters (r, h, m, Fav, At, i)? Hint: find the time at which it stops sliding, first.

Answer 1

1. 
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